Knowledge of the `true' relations can be used to make more accurate predictions of how the time series evolves in the future, e.g., by using graph neural networks (GNNs) (e.g., [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}) .
Even more, the graph can reveal fundamental insights into the system described by the time series, and may thus be of value in itself, independent of an improvement in the forecasting quality.
Therefore, recent works aim at jointly inferring relations between the time series and learn to forecast in an end-to-end manner, sometimes without any prior information about the graph [9]}, [10]}.
Besides potential benefits in forecasting quality, inferring a graph among \(N\)  time series comes at an inherent computational complexity of \(O(N^2)\) , which needs to be taken into account when deciding whether to leverage joint graph inference and forecasting. Hence, we consider the following research questions in this paper.
